In this technical report, the systematic investigation of lattice-valued possibilistic measures, opened in the first part of this report (cf. Technical Report No. 952, ICS AS CR, December 2005) is pursued and focused towards possibilistic variants of the notions of outer (upper) and lower (inner) possibilistic measures induced by a given partial possibilistic measure. The notion of Lebesgue mea...

Several recent studies have been devoted to investigating the limitations that ordinary quantum mechanics and/or quantum gravity might impose on the measurability of space-time observables. These analyses are often confined to the simplified context of two-dimensional flat space-time and rely on a simple procedure for the measurement of space-like distances based on the exchange of light signal...

A wide range of metrology processes are involved in the manufacture of large products. In addition to the traditional tool setting and product verification operations increasingly flexible metrology enabled automation is also being used. Faced with many possible measurement problems and a very large number of metrology instruments, employing diverse technologies, the selection of the appropriat...

The well-known Conley’s theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow φ on the compact metric space X , i.e. X − CR(φ) = ⋃ [B(A) − A], where CR(φ) denotes the chain recurrent set of φ, A stands for an attractor and B(A) is the basin determined by A. In this paper we show that by appropriately selecting the definition of random at...

1 Sigma-Algebra: Describing measurable sets 6 1.1 Families of sets . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Semiring of sets . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Restricted algebras . . . . . . . . . . . . . . . . . . . . 10 1.1.3 Sigma Algebras . . . . . . . . . . . . . . . . . . . . . . 10 1.1.4 Binary Unions . . . . . . . . . . . . . . . . . . . . . . 12 1.1...

1 Describing measurable sets 8 1.1 Families of sets . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.1 Semiring of sets . . . . . . . . . . . . . . . . . . . . . . 9 1.1.2 Restricted algebras . . . . . . . . . . . . . . . . . . . . 12 1.1.3 Sigma Algebras . . . . . . . . . . . . . . . . . . . . . . 12 1.1.4 Binary Unions . . . . . . . . . . . . . . . . . . . . . . 14 1.1.5 Initial Sigm...